Abstract
This paper presents quadratic finite-volume methods for elliptic and parabolic problems on quadrilateral meshes that use Barlow points (optimal stress points) for dual partitions. Introducing Barlow points into the finite-volume formulations results in better approximation properties at the cost of loss of symmetry. The novel 'symmetrization' technique adopted in this paper allows us to derive optimal-order error estimates in the H1-and L2-norms for elliptic problems and in the L∞ (H1)-and L∞ (L2)-norms for parabolic problems. Superconvergence of the difference between the gradients of the finite-volume solution and the interpolant can also be derived. Numerical results confirm the proved error estimates.
Original language | English |
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Pages (from-to) | 1342-1364 |
Number of pages | 23 |
Journal | IMA Journal of Numerical Analysis |
Volume | 33 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Oct 2013 |
Keywords
- Barlow points
- elliptic boundary value problems
- error estimation
- finite-volume element methods
- parabolic equations
- quadrilateral meshes
ASJC Scopus subject areas
- General Mathematics
- Computational Mathematics
- Applied Mathematics